Although considerable attention has been given to zero-inflated count data, research on zero-inflated lognormal data is limited. In this article, we consider a study to examine human sperm cell DNA damage obtained from single-cell electrophoresis (COMET assay) experiment in which the outcome measures present a typical example of log-normal data with excess zeros. The problem is further complicated by the fact that each study subject has multiple outcomes at each of up to three visits separated by six-week intervals. Previous methods for zero-inflated log-normal data are based on either simple experimental designs, where comparison of means of zero-inflated log-normal data across different experiment groups is of primary interest, or longitudinal measurements, where only one observation is available for each subject at each visit. Their methods cannot be applied when multiple observations per visit are possible and both inter- and intra-subject variations are present. Our zero-inflated model extends the previous methods by incorporating a hierarchical structure using latent random variables to take into account both inter- and intra-subject variations in zero-inflated log-normal data. An EM algorithm has been developed to obtain the Maximum likelihood estimates of the parameters and their standard errors can be estimated by parametric bootstrap. The model is illustrated using the COMET assay data.